Journal of Global Optimization

, Volume 49, Issue 4, pp 623–649 | Cite as

Branching on hyperplane methods for mixed integer linear and convex programming using adjoint lattices

Article

Abstract

We present branching-on-hyperplane methods for solving mixed integer linear and mixed integer convex programs. In particular, we formulate the problem of finding a good branching hyperplane using a novel concept of adjoint lattice. We also reformulate the problem of rounding a continuous solution to a mixed integer solution. A worst case complexity of a Lenstra-type algorithm is established using an approximate log-barrier center to obtain an ellipsoidal rounding of the feasible set. The results for the mixed integer convex programming also establish a complexity result for the mixed integer second order cone programming and mixed integer semidefinite programming feasibility problems as a special case. Our results motivate an alternative reformulation technique and a branching heuristic using a generalized (e.g., ellipsoidal) norm reduced basis available at the root node.

Keywords

Linear programming Volumetric center Analytic center Interior point methods Convex programming Mixed integer programming Lattice basis reduction 

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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Management Sciences, Robert R. McCormick School of EngineeringNorthwestern UniversityEvanstonUSA

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